Failure characteristic and acoustic emission spatio‐temporal evolution of coal under different cyclic loading rates

The coal and rock dynamic disasters occur more and more frequently in deep mining, which is tightly correlated to the instability of coal pillars under high stress and cyclic disturbance load. In this study, the strength, deformation behaviors, and failure mechanism of coal under cyclic loading in a high‐stress state were investigated by considering the influence of cyclic loading rate. The experimental results indicate that the compressive strength is positively correlated with the cyclic loading rate, and the deformation patterns, AE amplitude, and spatial evolution are the same under various cyclic loading rates. The damage variable shows the “slow increase→fast increase→slow increase→ fast increase →slow increase→fast increase→rapid increase” trend. The damage growth rate ranges from 9.32 × 10−5 to 4.86 × 10−3, and increases with the cyclic loading rate. The spatial fractal dimensions under various cyclic loading rates are the same, and the distribution ranges from 2.1 to 2.9, showing a general downward trend. The microfailure mechanism under various cyclic loading rates is mixed failure dominated by tensile failure, with a small amount of shear failure. There is a positive correlation between the percentage of shear cracks and the cyclic loading rates.


| INTRODUCTION
With the increasing depth of coal mining, deep mining is faced with the complex geological conditions of high crustal stress and strong mining disturbance, and coal and rock dynamic disasters occur frequently. 1,2 Dynamic disasters are tightly correlated to the instability of the coal pillar. 3 Deep coal pillar is in a state of high crustal stress for a long time and is affected by strong disturbance loads such as artificial blasting, large-scale roof breaking, and fault sliding during the mining process. Local coal pillars have been damaged, resulting in the overall instability of the coal pillar, with the rapid energy release of the coal pillar. Thus, the investigation of the failure characteristics and mechanism of high-stress coal under disturbance is of significance in evaluating the stability of deep coal pillars and the prevention of dynamic disasters.
To date, the mechanical behaviors and failure mechanisms of rock and rock-like materials under disturbance load (cyclic loading and unloading) have been intensively investigated. 4,5 Erarslan and Williams 6 investigated the fracture toughness and damage mechanisms of Brisbane tuff disc specimens under static and cyclic loading. Meng et al. 7 studied the loading rate effect on acoustic emission (AE) and energy dissipation characteristics of sandstone during the cyclic loading test. The mechanical behaviors of rock-like materials were investigated with various initial stress levels and loading rates. 8 Zhou et al. 9 proposed a modified damage variable to analyze the correlation between the damage variable and strain rate under dynamic cyclic loading. The influence of loading rate and frequency on the mechanical properties and failure mode of T-shaped cross fissures samples was observed under uniaxial cyclic loading compression. 10 Sun et al. 11 clarified the influence of dynamic cyclic load on the hydraulic conductivity of soft clay based on seepage tests. The fatigue failure patterns of water-bearing sandstone under cyclic loading were investigated with various amplitude levels and loading frequencies based on the numerical simulation method. 12 Xin et al. 13 studied the porosity and permeability of coal with different cyclic paths. Peng et al. 14 analyzed the energy dissipation and crack propagation modes of fractured sandstone with different cyclic gradient loading conditions. Sun and Yang 15 investigated the effect of cyclic frequencies on energy and damage characteristics of sandstone during the cyclic loading test. The crack opening stress was calculated under tension-compression cyclic load. 16 Chen et al. 17 analyzed the fracture mechanisms of three-point bending notched granite beams during the prepeak and post-peak cyclic loading tests based on AE and digital image correlation (DIC) methods. Elbably et al. 18 revealed the deformation and failure patterns of encased steel-high-strength concrete columns subjected to axial and cyclic loading. The damage and failure patterns of coal were analyzed based on true triaxial cyclic loading tests. 19 Sun et al. 20 investigated the influence of water content on fatigue deformation, energy dissipation, and failure mode of concrete under compressive cyclic loads. The dynamic compression properties, damage, and fracture patterns of sandstone after freeze-thaw cycles were analyzed. 21 Zhou et al. 22,23 studied the mechanical properties and established a dynamic constitutive model during the true triaxial dynamic cyclic loading test with various loading rates. These studies are of great significance in understanding the mechanical behavior and failure mechanism of rock and rock-like materials under disturbance load, while few studies involve the strong bump-prone coal and the disturbance failure characteristics in a high-stress state.
AE technology, a real-time and non-destructive testing method, is commonly applied to characterize the deformation and failure patterns of rock and soil material. Xie et al. 24 investigated the AE spatial fractal characteristic of bedded rock salt under uniaxial compression and indirect tension conditions. Meng et al. 7 analyzed the loading rate effect on AE and energy dissipation of sandstone under cyclic loading. Chen et al. 17 studied the failure mechanisms of three-point bending notched granite beams subjected to cyclic loading based on AE and DIC methods. Li et al. 25 analyzed the strength and AE evolution of coal with a pre-existing fissure under uniaxial compression. Wang et al. 26 identified the failure points of limestone using the tangent damage factor (TDF) based on the AE signals. The deformation behaviors and AE evolution of weakly cemented sandstone from Shendong Coalfield were analyzed. [27][28][29] Liu et al. 30 studied the effect of loading rate on tensile properties and multiparameter characteristics of coal. Dou et al. 31 investigated the mechanical behavior and AE evolution of sandstone with various inclined precracks. Du et al. 32 studied the mechanical behavior and AE evolution of rock under direct shear and variable angle shear conditions. Shen et al. 33 analyzed the AE amplitude-frequency patterns and frequency band during the loading process of coal under different water pressure. He et al. 34 discussed the AE signal "quiet period" before the coal and rock failure. Du et al. 35 investigated the AE evolution and crack classification under several basic laboratory rock tests. Zhao et al. 36,37 analyzed the strength, fracture patterns, and failure mechanism of bedding coal under modes I and II loading conditions based on the DIC and AE methods.
The above studies focus on the mechanical behaviors and failure mechanism of rocks and rock-like materials under cyclic disturbance, while few studies involve the strong bump-prone coal and the disturbance failure characteristics in a high-stress state. Thus, it is urgent to study the failure characteristics and AE evolution of high-stress coal under disturbance. In this study, cyclic loading tests were performed for strong bump-prone coal in a high-stress state with various cyclic loading rates, and the AE signals were monitored simultaneously. The strength, deformation characteristics, and AE spatiotemporal evolution were investigated, and the evolution of damage and AE spatial fractal dimension and the microfailure mechanism was studied. This study provides a basis for the early warning and prevention of deep coal and rock dynamic disasters.

| Coal specimen preparation
The coal specimens were collected from the 3 −1 101 haulage roadway of the Hongqinghe Coal Mine in Xinjie coalfield, China. The 3 −1 coal seam belongs to non-stick coal with an average thickness of 6.23 m, inclination angle of 2°, and average buried depth of 718.60 m. The coal seam has a strong bump-prone tendency. 38 The microscopic composition of the coal specimen is mainly vitrinite, and the second is the fusinoid group. Xray diffraction test indicated that the mineral percentage of quartz is 15.0%, clay minerals 15.0%, calcite 12.0%, plagioclase 8.0%, pyrite 1.0%, and other amorphous 49.0%. The uniaxial compressive strength (UCS) of the coal specimen is 24.65 MPa. The fresh, flat, and complete coal blocks were processed into standard cylinder specimens (Φ 50 mm × H 100 mm), and the two end faces were polished to meet parallel accuracy. The diameter, height, and density of coal specimens are shown in Table 1.

| Microstructure characteristics of coal specimens
Computerized tomography (CT) can analyze the internal microstructure of the target object, and is the common test method in the rock mechanics field. CT scanning tests were performed by using an industrial CT system. As shown in Figure 1, the structural features of different sections are quite different, and there are many layered fillings and a small number of white inclusions. The phenomenon indicates that the coal samples have strong heterogeneity due to the differences in the microstructure at different sections. Thus, the strength and deformation behaviors of coal samples are quite different.

| Test equipment
As shown in Figure 2, the rock testing machine, AE monitoring system, and strain gauge system were conducted in this study. The maximum axial load of the rock testing machine is 300 kN, and the lateral displacement rate varies from 0.001 to 254 mm/min. The AE monitoring system, equipped with a maximum of eight channels, can record and investigate the AE signals and related parameters during the damage and failure process. The strain gauge system was equipped with a maximum of 16 channels, and the sampling frequency can reach 1 MHz.

| Test scheme
To monitor the internal damage and failure characteristics of the specimen, six AE sensors (Model: Nano 30) were attached to the specimen surface according to the Geiger algorithm, 39 and Vaseline is used for coupling between the specimen surface and the AE sensors. The two strain gauges were attached to the middle of the back of the specimen (Figure 2). The loading path of the cyclic loading test was as follows (Figure 3). The coal specimen was loaded to 30 kN at a constant rate of 0.60 mm/min during the initial loading phase (OA), and then the load is maintained for 20 s at the load holding phase (AB). Then different displacement rates were used for cyclic loading and unloading during the cyclic disturbance phase (BC), the rates were 0.30, 0.60, 3.00, 6.00, and 30.00 mm/min, the cyclic amplitude was 10 kN, and the cyclic count was 10 times. After the cyclic loading, the specimen was loaded at the displacement rate of 0.60 mm/min until complete failure (CDE). According to the cyclic loading rate, the test was divided into five groups, with four specimens in each group. The materials testing machine system, AE monitoring system, and strain gauge system were started and stopped synchronously.

| Deformation evolution characteristics
As shown in Table 1, the compressive strength was obtained based on the compressive strength formula. The compressive strength of the coal specimen under cyclic loading conditions is higher than the UCS, which is caused by the compaction of internal pores and fissures during the cyclic disturbance phase. As a whole, the compressive strength increased with the cyclic loading rate, and the compressive strength increased greatly when the cyclic loading rate reaches 30.00 mm/min. Previous research has proved that the correlation between compressive strength and loading rate can be described by linear, exponential, logarithmic, and power functions. 40 As shown in Figure 4, the correlation between compressive strength and cyclic loading rate can be also expressed by the above functions. Among them, the fitting degree of the logarithmic function and exponential function was high, while the fitting degree of the power function was low. However, the dispersion of compressive strength was high caused by the anisotropy and heterogeneity of coal specimens, and the dispersion increased with the cyclic loading rate. Figure 5 shows that the deformation evolution of typical coal specimens under various cyclic loading rates was the same and similar to those under uniaxial compression. At the initial loading stage, the curve was concave due to internal initial fissures and pores compaction. Then the stress increases linearly with strain during the elastic stage. The stress-strain curve coincided with the cyclic disturbance phase, indicating that only a small amount of damage and failure generate during the cyclic disturbance phase, corresponding to the initiation of a few microcracks. After the cyclic disturbance phase, the stress increases fast with large numbers of microcracks generated, and many microcracks propagated and coalesced. The microcracks propagated and coalesced rapidly to form macrocracks near the peak load, and then the load dropped suddenly. The dispersion of axial strain is large at different cyclic loading rates due to the anisotropy and heterogeneity of coal specimens. Figure 6 shows the evolution of stress and AE amplitude of coal specimens under cyclic loading with time, and the AE amplitude distribution of coal specimens under various cyclic loading rates was the same. Only few AE events were detected in the crack compaction stage, mainly due to the closure and compaction of initial pores and fissures, and the amplitude was mainly distributed in 40-80 dB. Then many AE events were generated during the linear elastic stage, with an amplitude distribution of 40-100 dB. Next, a few AE events were generated at the load-holding phase, with an amplitude of 40-100 dB. At the cyclic disturbance phase, many AE events were generated during the first loading stage, with an amplitude of 40-100 dB, while a few AE events were generated in the unloading stage, with an amplitude of 40-80 dB. The AE events generated during the loading and unloading stages decreased slowly with the increasing counts of disturbances. The AE events at low cyclic loading rate are mainly concentrated in the previous loading and unloading processes, and the AE events appear more in the subsequent loading and unloading process with the increase of cyclic loading rate. The phenomenon indicates that the high cyclic loading rate aggravates the damage process, and more AE events appear in the subsequent loading and unloading process. After the cyclic disturbance phase, many AE events were generated, with amplitudes ranging from 40 to 100 dB. When approaching the peak load, many AE events were generated, with amplitudes ranging from 40 to 100 dB. However, there were few AE events generated during the cyclic disturbance phase with an amplitude of 40-80 dB at the cyclic loading rates of 0.30 and 0.60 mm/min, while many AE events were generated with an amplitude of 40-100 dB at the cyclic loading rates of 3.00, 6.00, and 30.00 mm/min.  To understand the influence of cyclic loading rate on the AE amplitude, the distribution of AE amplitude during the cyclic disturbance phase is shown in Figure 7. The AE amplitude was mainly concentrated on 50-60 and 60-70 dB, and their percentages were more than 25%. The percentages of AE amplitude in the range of 40-50 and 70-80 dB range from 5% to 20%, and few AE amplitudes were in the range of 80-90 and 90-100 dB. However, the AE amplitude varies with different cyclic loading rates. The percentage of high AE amplitude (80-100 dB) was lowest at the cyclic loading rate of 0.60 mm/min, indicating that few macrocracks were generated during the cyclic disturbance phase. The main reason is that the cyclic disturbance phase is located in the elastic stage. There is no obvious correlation between the AE amplitude and cyclic loading rate, and the differences are mainly caused by the anisotropy and heterogeneity of coal specimens.

| Damage evolution
AE waveform generated during the deformation and damage process can characterize the evolution of internal crack initiation, propagation, and penetration failure. AE parameters (such as AE hit rate and AE energy) were commonly applied to quantitatively express the evolution characteristics of damage variables in the whole deformation and damage process. 26  As shown in Figure 6, the damage variable increased slowly at the crack compaction stage, which is mainly due to the closure and compaction of initial pores and fissures. Then the damage variable increased at the linear elastic stage and increased slowly at the load-holding phase. At the cyclic disturbance phase, the damage variable increased fast at the first loading stage and then increased slowly in the loading and unloading stages. After the cyclic disturbance phase, the damage variable increased fast. When approaching the peak load, the damage variable increased rapidly. However, the initial and final damage variable (damage variable at the beginning and end of the cyclic disturbance phase) increased with the cyclic loading rate, while the damage increase (the increment between the initial and final damage variable) varied at different cyclic loading rates. To understand the influence of cyclic loading rate on the rate of damage increase, the damage growth rate (G D ) was defined as follows: where D Δ is the damage increase, and T is the time of the cyclic disturbance phase.
As shown in Figure 8, the damage growth rate ranged from 9.32 × 10 −5 to 4.86 × 10 −3 , and increased with the cyclic loading rate. The phenomenon indicates that the high cyclic loading rate aggravates the damage process, and shortens the failure time. Therefore, the high frequency and amplitude disturbance should be avoided in coal pillar disaster prevention, and corresponding measures should be taken in engineering practice.

| AE spatial evolution
The spatial evolution of AE events reflects the crack initiation and propagation inside specimens, and the internal microcracks can be determined by the location of AE event sources. 39,41 To study the internal crack propagation of coal specimens under cyclic loading, the endpoints of the initial loading phase (A), load holding phase (B) and cyclic disturbance phase (C), the peak stress point (D), and the end point of loading (E) were selected for analysis, respectively. According to the Geiger localization algorithm, AE event location was obtained. Figures 9 and 10 show the AE events spatial characteristics of coal specimens under cyclic loading, and the spatial characteristics were the same under different loading rates. At the initial loading phase, many AE events were generated in the middle of the coal specimen, with the amplitude concentrated in 40-80 dB. The main reason is that the initial fissures and pores inner the coal specimen was closured and compacted. With the increase in load, a small number of AE events occurred in the middle of the coal specimen, with an amplitude of 40-100 dB. Then, few AE events were generated during the cyclic disturbance phase, with the amplitude mainly distributed in 40-80 dB and a small amount occurring in 80-100 dB. After the cyclic disturbance phase, many AE events were generated, with an amplitude of 40-100 dB. After the peak load, the coal F I G U R E 7 Distribution of acoustic emission amplitude during the cyclic disturbance phase with different cyclic loading rates.
F I G U R E 8 Distribution of damage variable during the cyclic disturbance phase with different cyclic loading rates. specimen burst instantaneously, and only a few AE events were detected due to part of the AE sensors falling off. However, few AE events occurred during the cyclic disturbance phase when the cyclic loading rate was low (0.30 and 0.60 mm/min), with an amplitude of 40-80 dB. While more AE events were generated with an amplitude of 40-100 dB at the high cyclic loading rates (3.00, 6.00, and 30.00 mm/min).
Previous studies have proven that AE sequences generated in the deformation and failure process have fractal characteristics in time and space. 25,42,43 The spherical covering method, projection circle covering method, and cylindrical covering method are used to obtain the spatial fractal dimension of AE events. The cylindrical-covering method is commonly used to obtain the spatial fractal dimension of cylinder samples, 24,41,44 and the spatial fractal dimension of coal under various cyclic loading rates was obtained. Figure 11 shows that the spatial fractal dimension of coal samples under various cyclic loading rates was the same, and generally presented a downward trend, which is the same as previous results under the uniaxial compression tests. 24,41,44 The fractal dimension of the initial loading phase was high, mainly distributed in 2.7-2.9, indicating that the initial fissures and pores in the coal sample were evenly distributed, and the AE events generated were evenly distributed. At the load-holding phase, the fractal dimension decreased slowly, mainly distributed in 2.6-2.8, which is mainly due to the microcrack initiation inside the coal sample. During the cyclic disturbance phase, the fractal dimension decreased to 2.5-2.7. The main reason is that the disturbance led to the initiation and propagation of microcracks. Then the fractal dimension decreased rapidly, and the distribution ranged from 2.3 to 2.4, which was mainly due to the propagation and coalescence of internal microcracks. When approaching the peak load, the microcracks rapidly propagated and coalesced to form a macroscopic fracture surface, and the fractal dimension is reduced to a minimum, which was distributed in 2.1-2.3. Due to the high anisotropy of coal samples, there are some differences in AE spatial fractal dimensions.

| Microfailure mechanism
The microfailure mechanism can be analyzed by the AE signals detected during the damage process. 35 Previous studies have shown that different types of cracks correspond to different AE signals. In general, the waveforms with high AF (average frequency) and low RA (rise time/amplitude) represent tensile cracks, while the waveforms with low AF and high RA represent shear cracks. The mixed tension-shear cracks are low AF and low RA waveforms. 35,38 Figure 12 shows the AF-RA density maps of coal under various cyclic loading rates. The AF range of coal under various cyclic loading rates was the same, ranging from 0 to 750 kHz. There were some differences in the distribution of RA. When the loading rate was 0.30 mm/ min, the RA was mainly distributed in 0-100 μs/dB, and a small amount was distributed in 125-200 μs/dB.
The main distribution was 0-225 μs/dB at 0.60 mm/ min, with a small amount of around 350 μs/dB. The main distribution was 0-300 μs/dB at 3.00 mm/min, and a small amount was 400-650 μs/dB. The main distribution was 0-400 μs/dB at 6.00 mm/min, with a small amount of around 500 μs/dB. The main distribution was 0-450 μs/dB at 30.00 mm/min, and a small amount was around 600 μs/dB.
According to the AF-RA data density maps under different cyclic loading rates, the black dotted line (AF = 4 RA) was a reference line to determine the crack failure mode. The AF-RA data (red area) are mainly concentrated in the area of low RA and low RA and low AF, with only a small amount of low AF, namely the microfailure mechanism of coal samples under various cyclic loading rates is the mixed tension-shear failure with few shear failures. However, there exist many differences in the AF-RA distribution of coal samples under various cyclic loading rates. The data points close to the horizontal axis (low AF) gradually increase with the increasing cyclic loading rate. The phenomenon indicates that the percentage of shear cracks increases with the cyclic loading rate, and is positively correlated with the cyclic loading rate. The main reason is that the high cyclic loading rate aggravates the failure process, the cracks are not recovered during the unloading stage, and shear failure occurs at the next loading stage.

| CONCLUSIONS
From the above analysis and discussions, the main conclusions are as follows: (1) The compressive strength of coal increases with the cyclic loading rate and increases greatly when the cyclic loading rate reaches 30.0 mm/min. The correlation between compressive strength and cyclic loading rate can be well expressed by linear, exponential, logarithmic, and power functions. The deformation patterns of coal specimens under various cyclic loading rates were the same and similar to those under uniaxial compression. (2) The AE amplitude and spatial evolution of coal under various cyclic loading rates were the same. The AE amplitude was mainly concentrated on 50-60 and 60-70 dB, and their percentages were more than 25%. The percentages of AE amplitude in the range of 40-50 and 70-80 dB range from 5% to 20%, and few AE amplitudes were in the range of 80-90 and 90-100 dB. (3) The damage variable increased slowly and then increased fast at the initial loading phase, and increased slowly during the load-holding phase. At the cyclic disturbance phase, the damage variable increased fast at the first loading stage and then increased slowly in the loading and unloading stages. The damage variable increased fast after the cyclic disturbance phase, and the damage variable increased sharply near the peak load. The damage growth rate ranged from 9.32 × 10 −5 to 4.86 × 10 −3 , and increased with the cyclic loading rate.